To state the obvious, turning the AC on puts a higher load on the front pulleys including the one that runs the alternator.
It also puts a higher load on the cars electrical system as it energizes a clutch pack on the AC pump and runs the rest of the system (fans internal/external, drier, controls etc.)
So anyway, moral of the story is... Put an earth kit together and strap it to all the right places. That should fix it.
There are about 1000 wires connected to the positive circuit and one 20 year old earth strap that bolts onto the body and motor in 1 spot each (assuming your car still has factory earthing). As we learn in high school science, energy cannot be created or destroyed, only transferred. So in theory there's no where near the same return wiring as there are wires drawing away from the battery. Its a circuit, that's how it works (don't flame me saying you know, I'm putting it out there for future readers who might not).
GL